Stochastically Forced Compressible Fluid Flows (De Gruyter Series in Applied and Numerical Mathematics)

by Dominic Breit, Eduard Feireisl, and Martina Hofmanova

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This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality.





Contents
Part I: Preliminary results
Elements of functional analysis
Elements of stochastic analysis



Part II: Existence theory
Modeling fluid motion subject to random effects
Global existence
Local well-posedness
Relative energy inequality and weak-strong uniqueness



Part III: Applications
Stationary solutions
Singular limits
  • ISBN10 3110490765
  • ISBN13 9783110490763
  • Publish Date 22 January 2018
  • Publish Status Active
  • Publish Country DE
  • Imprint De Gruyter